“Happy Days,” the series that taught future generations the poetry of “Blueberry Hill” and the power of telling frenemies to “sit on it,” has a more dubious claim to history. In 1977, desperate writers decided to fly the Fonz into Hollywood for a screen test — and a chance to accept an absurd water-ski challenge. While the series would continue to run for seven more years, it never recovered creatively from the stunt.

But while you’re reminiscing about that “jump the shark” moment, take a moment to celebrate the show’s much savvier, and equally telling move. Let’s call it “Chucking it away.”

The sitcom, which debuted in 1974, originally introduced viewers to oldest son Chuck Cunningham, a towering jock who seemed to stop by the house only for a free meal and a quick shower. Early in the second season, he went out to play basketball and never came back. The series rarely referred to him again, leaving more screen time to the Fonz, who was originally created to be a background player.

“Days” isn’t the only series to reboot itself in front of our eyes.

“Newhart” switched from videotape to film during its second season while replacing supporting characters with a snotty maid and a trio of woodsmen. After some unintended drama behind the scenes of “NYPD Blue,” David Caruso was replaced by the kinder and gentler Jimmy Smits. After a pilot for “Seinfeld” failed to impress viewers or network execs, a female character named Elaine Benes was added to the mix. Each of those series thrived from the changes.

Getting a mulligan has been harder to come by in recent years. As network executives fight viewer erosion, they’re more prone to cancel struggling series quickly instead of bothering to fix them.

But that trend may be changing. Fox’s “The Mindy Project,” which initially failed to live up to creator Mindy Kaling’s potential, has done a major cast reshuffle, eliminating characters with little to do and elevating roles that appear to be clicking. “Up All Night,” starring the immensely talented trio of Maya Rudolph, Will Arnett and Christina Applegate, is in the midst of a hiatus, a term that usually translates into “Dead Show Walking.” Instead, the series is expected to return in April to NBC with major changes, including a plan to film with multiple cameras in front of a studio audience.

And then there’s NBC’s “Smash,” last year’s heavily promoted musical comedy that managed to be both exhilarating and excruciating. The show returns this Tuesday with new show runner Joshua Safran and it’s obvious that his last gig was supervising “Gossip Girl.” Out is Uma Thurman; in is red-hot Jennifer Hudson. Out are solid relationships; in is an endless stream of hot, single Broadway babies who spend more time flirting than practicing their dance numbers.

Why this string of second chances? Four words: “The Big Bang Theory.”

The show was conceived as a sitcom about two physicists who befriend a fetching new girl. She proceeds to take advantage of their naive ways and cons her way into their apartment. CBS passed on this version, but continued to develop it with creators Chuck Lorre and Bill Prady for two years. The female character was reshaped and recast, leading to one of the most successful programs on TV today.

Networks have to be looking at that boffo scenario and believing that sometimes tinkering instead of tanking is the way to go — even if it means making a Chuck Cunningham disappear.

Neal Justin • 612-673-7431

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Uma Thurman is out and Jennifer Hudson (left, with Katharine McPhee) is in on “Smash.”